What is the Greatest Common Factor of 20475 and 20480?

Greatest common factor (GCF) of 20475 and 20480 is 5.

GCF(20475,20480) = 5

We will now calculate the prime factors of 20475 and 20480, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20475 and 20480.

How to find the GCF of 20475 and 20480?

We will first find the prime factorization of 20475 and 20480. After we will calculate the factors of 20475 and 20480 and find the biggest common factor number .

Step-1: Prime Factorization of 20475

Prime factors of 20475 are 3, 5, 7, 13. Prime factorization of 20475 in exponential form is:

20475 = 3² × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 20480

Prime factors of 20480 are 2, 5. Prime factorization of 20480 in exponential form is:

20480 = 2¹² × 5¹

Step-3: Factors of 20475

List of positive integer factors of 20475 that divides 20475 without a remainder.

1, 3, 5, 7, 9, 13, 15, 21, 25, 35, 39, 45, 63, 65, 75, 91, 105, 117, 175, 195, 225, 273, 315, 325, 455, 525, 585, 819, 975, 1365, 1575, 2275, 2925, 4095, 6825

Step-4: Factors of 20480

List of positive integer factors of 20480 that divides 20475 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 4096, 5120, 10240

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20475 and 20480. The biggest common factor number is the GCF number.
So the greatest common factor 20475 and 20480 is 5.

Also check out the Least Common Multiple of 20475 and 20480